Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until it is al dente.
Meanwhile, melt half the butter in a frying pan, add the breadcrumbs and cook, stirring frequently, for 5 minutes until golden and crisp. Transfer the crumbs to a bowl and leave to cool slightly then stir in the Parmesan cheese.
Melt the remaining butter in a large saucepan or wok over a low heat, add the shallots and garlic and cook, stirring occasionally, for 5 minutes, or until softened. Add the radicchio and lemon juice and season with salt and pepper. Cook, stirring, for 2 minutes, or until the radicchio has wilted.
Drain the pasta, reserving 2 tablespoons of the cooking water. Add the pasta and the reserved cooking water to the radicchio mixture and toss briefly over the heat. Serve immediately is small serving bowls, topped with the cheese crumbs.